Cremona's table of elliptic curves

1386 = 2 · 3² · 7 · 11

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 11+	Signs for the Atkin-Lehner involutions
Class	1386h	Isogeny class
Conductor	1386	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-9879408 = -1 · 24 · 36 · 7 · 112	Discriminant
Eigenvalues	2- 3- -2 7+ 11+ -4  0  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-131,627]	[a1,a2,a3,a4,a6]
Generators	[5:6:1]	Generators of the group modulo torsion
j	-338608873/13552	j-invariant
L	3.4313164160578	L(r)(E,1)/r!
Ω	2.2768188650059	Real period
R	0.37676651278635	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	11088cb1 44352bm1 154c1 34650ba1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1386h1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	-	-2	+	+	-4	0	4	-4	-2	-10	-6	0	-4	-10	14	-10	-8	8	4	4	16	-4	-10	6

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Quadratic twists for elliptic curve 1386h1

-4	8	-3	5	-7	-11
11088cb1	44352bm1	154c1	34650ba1	9702bw1	15246s1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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